For more than 20 years, Radiohead’s music has oriented around fear. They ping-pong between the poles of personal anxiety and global geopolitical concern, but most often occupy a space somewhere in between. Yet despite their fearful fixations, Radiohead have earned a massive following, becoming our fin de siècle arena rock band.

Of the headliners at this year’s Lollapalooza, Radiohead stand out. Not only did they perform a two-hour set, the longest of the entire four-day festival (and they ended up stretching it 15 minutes past curfew), but their music is uniquely suited to the paradox of feeling alienated in a crowd of 100,000 people outside on a beautiful night in July. In the packed field in front of the Samsung stage, I talk with fans who have flown out from Florida and Pennsylvania just to see this band whose work belies togetherness and connection. The biggest sing-along of the night roars at the very end of the set, during a song about feeling policed, to the lyrics, “I lost myself, I lost myself."

Radiohead come from the United Kingdom, not the United States, but they’ve built a career on peering into this country from across the Atlantic. They were still playing clubs in England by the time they broke into American arenas. Unlike Oasis or Blur, bands once considered their Britrock peers, Radiohead had little use for stoking nationalist sentiment or having any fun on the Isle. During the bandmembers’ lifetime, England has seen a huge expansion of mass electronic surveillance by police, an idea that stokes the rightful paranoia that is the heart of Radiohead’s work — and one that has given them a shared language with which to connect to America and Americans in our modern, war-borne, post-9/11 age.

The band’s breakthrough began with The Bends, followed by the angsty and erratic OK Computer, followed by the almost unrecognizable electronic meditation Kid A. For a week in 2000, Kid A topped the Billboard 200, right above albums by Mystikal, Nelly, Green Day, and 98 Degrees.

Most music at the top of the US charts in 2000 reflected a need to be distracted by light entertainment (this was the year of “Who Let the Dogs Out?”) or comforted (Creed’s songs about God’s unconditional love blasted daily through Top 40 stations). Radiohead, with their jazzy bass lines and their imp-poet frontman and their fucking harp parts, chose instead to perturb and pick at our scabs.

Now, almost 16 years after Kid A fell out of the sky, Radiohead sneak onstage at Lollapalooza. It’s their second time headlining, the last being in 2008, right after their pay-what-you-want surprise album In Rainbows came out. This time they’re touring A Moon Shaped Pool, an orchestral breakup LP steeped in ambient dread.

The first voice we hear onstage isn’t Yorke’s, but Nina Simone’s: An interview with the legendary singer plays in which she discusses the meaning of freedom. “What does freedom mean?” the interviewer asks. “It’s only a feeling,” Simone replies. Then she clarifies, “I’ll tell you what freedom is to me: No fear.” Two drummers carefully, patiently set up, and then Radiohead launches into “Burn the Witch,” a song written a decade ago that finally found its place at the head of their new record.

Powered by strings on the studio version, “Burn the Witch” takes on a wiry, lean quality played live. Radiohead don’t take the shortcut of playing prerecorded samples; instead, multi-instrumentalist Jonny Greenwood bows his guitar in between tinkering with a shelf full of synthesizers. Thom Yorke, in all his scruffy boy-poet glory, walks out in full rock star regalia: black jeans opened neatly at the knees, loose black t-shirt, black leather jacket, black Chuck Taylor–inspired zip-up boots. He’s the picture of cool confidence, hardly looking like someone who wrestles with personal terror thoughts for a living.

Yorke is 47, with long graying hair bunned up behind his skull and an amorphous sea of stubble roiling across his face. He’s small, like 5-foot-5, and sounds best singing in a high, feminine register, which has helped him secure his weird position as the anti-rock-star rock star. He has charisma onstage but no bravado; for the first hour and 45 minutes of the set, he only addresses the audience in chirps and silly voices, in nonsensical asides or plain gibberish. At one point he says “Gracias, amigos” in a sarcastic Castilian accent. Knowing how difficult it is to engage meaningfully in conversation with 100,000 people at once, he doesn’t bother.

More than a singer, Yorke’s a bandleader, and his interactions with his bandmates are just as fascinating to watch as his demonic dancing. He’ll punch out a rhythm in the air, or he’ll run over to Greenwood’s synth stack and tweak a knob if something doesn’t sound right. Sometimes he straps on a guitar and hammers out chords; during “Ful Stop,” a bass-driven groove off the new LP, he cradles a tiny keyboard in his left hand like it’s his dance partner and mashes the keys with his right.

He’s with his bandmates but apart from them, the only one dancing, the only one addressing the audience, the only one who seems aware that there’s an audience at all.

Yorke makes the perfect avatar for people who feel alone even amid this teeming crowd. His songs paint vibrant, full-spectrum portraits of the extremes of isolation, whether it’s sparked by romantic heartbreak (like most of A Moon Shaped Pool) or numbing political despair (like the rest of Radiohead’s catalogue).

Radiohead follow the first three songs off Pool with “2 + 2 = 5” and “Myxomatosis," from their Bush-era record Hail to the Thief. Not all the music that came out of that presidency has aged well, but Thief has. It avoids the specificity of explicit protest music, instead railing against broader machinations of power and its inevitable abuse. It’s an album about feeling sick to your stomach while everyone around you insists that everything is fine, that the wars waged on the news are just and worthwhile, that the economy isn’t teetering on the edge of collapse, that it’s fine, there there, it’s all OK.

There’s a release just in naming that sickness. Throughout his music, Yorke wrestles with the death drive — the desire that happens when the fear of living outweighs the fear of dying — as it manifests on both a personal and global scale. “No Surprises” has never sounded more like a suicide note than it does ringing out over Lollapalooza: “I’ll take a quiet life, a handshake of carbon monoxide ... This is my final fit, my final bellyache.” Later, “Idioteque” and its crazed beat play like a death knell for planet Earth: “Ice age coming, ice age coming ... We’re not scare-mongering, this is really happening."

It’s timely, especially given the next line of “Idioteque”: “Here I’m allowed everything all of the time." Each American presidential election dangles the promise of prosperity over its citizenry, despite all the evidence indicating that prosperity is only for the few, and not for long. The fulfillment of the American Dream appears again and again as a reward for selecting the right candidate: Pick the better politician and you too can claw your way to material security — all the way to a golden condo at the top of a gleaming tower with your name on it.

Those images of prosperity, hope, and happiness never show the flip side of material luxury: toxic pollution, record-breaking global temperatures, depleted resources. Deadly heat waves and poisoned water are presented at the debates as issues that run parallel to the pursuit of capital, as opposed to being direct effects of it. But when the pursuit of happiness depends on the exhaustion of the Earth, the life drive and the death drive get tangled.

Where can you go when the whole machine of humanity seems hell-bent on galloping into the fire? Maybe it’s not even a gallop; maybe it’s more like an ooze. No one can tell us when shit will really go down. The whole system we call Earth keeps rolling forward into the future, waiting for some natural cataclysm that no human decision can trigger or prevent.

Even in this strange and helpless moment, there’s music. There’s still Thom Yorke dancing, however helplessly, an anticapitalist and environmentalist on a stage sponsored by Samsung at one of the world’s most profitable music festivals. But he’s dancing. “This dance is like a weapon of self-defense against the present,” he sings on “Present Tense.” “As my world comes crashing down, I’ll be dancing.”

What else is there to do? We dance, too. Clouds have gathered over the park. Radiohead play “Identikit,” whose climax centers on the line “Broken hearts make it rain.” Yorke sings the words over and over again in his vulnerable falsetto, shaking his head, then tilting his face toward the sky. Right on cue, a few drops leak from above. I mean, it actually rains. We’re here waiting for a meteor, and the sky offers us water instead.